If you are competent, you have the necessary ability or skills to do something. If you can carry a heavy tray of food, and store a table's worth of orders in your head, you are probably a competent waitress.
The opposite of competent is incompetent––an incompetent travel agent might send you to Bahrain when you requested Britain. But competent on its own can sometimes be a veiled criticism, with the implication that someone competent is just going to through the motions––you'd rather have someone inspired on the job. In legal language, competent describes someone who is able to take part in a trial or sign a contract.
